By Geoffrey Hunter
This paintings makes on hand to readers with out really good education in arithmetic whole proofs of the elemental metatheorems of ordinary (i.e., essentially truth-functional) first order good judgment. integrated is an entire facts, available to non-mathematicians, of the undecidability of first order good judgment, an important truth approximately good judgment to emerge from the paintings of the final half-century.Hunter explains suggestions of arithmetic and set conception alongside the way in which for the advantage of non-mathematicians. He additionally offers plentiful routines with entire solutions.
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Additional info for Metalogic: An Introduction to the Metatheory of Standard First Order Logic
Example text
Y Frías Delgado, A. (1995), «Razonamiento no monótono: Un breve panorama»: Theoría, S. , vol. X/23, 7-26. Flach, P. y Kakas, A. ) (2000), Abductive and Inductive Reasoning: Essays on their Relation and Integration, Kluwer Academic Publishers, Applied Logic Series. Gentzen, G. (1969), The Collected Papers of Gerhard Gentzen, en M. E. Szabo (ed. ), North-Holland Publishing, Amsterdam/London. 41 A G U S T Í N R AY O Hintika, J. e Hintika, M. B. (1989), The Logic of Epistemology and the Epistemology of Logic, Kluwer Academic Publishers, Dordrecht.
11. )’ al lenguaje, e insistiendo que ‘el agua = H2O’ se sigue de ‘Verdadero(c)’, que a su vez se sigue de ‘Necesario(c)’. Tarski probó que cualquier teoría (suficientemente fuerte) en la que pueda probarse cada enunciado que resulte de reemplazar el nombre de una proposición por ‘d’ y un enunciado expresando esa proposición por ‘x’ en ‘Verdadero(d) ≡ x’ es inconsistente. 12. Para una exposición de las características formales de este tipo de lenguajes, véase Chellas, 1980. Para una exposición acerca de la importancia filosófica de este tipo de lenguajes ver Lewis, 1986.
Más aún, a pesar de que Husserl no realizó ninguna contribución específica a la lógica como ciencia, su fenomenología tuvo una gran influencia en el pensamiento lógico posterior, originando una concepción idealista de la lógica que se plasmó en los manuales de principios del siglo XX, entre los que cabe citar principalmente el de A. Pfänder, titulado Logik, de 1921 y otros textos menores. Éstos se extendieron a otras latitudes y, aunque en otros países ya se había impuesto la nueva lógica matemática, en los de habla hispana rigieron el enfoque y la 57 GLADYS PALAU enseñanza de la lógica hasta la segunda mitad del siglo XX.